16. ILLUSTRATIVE EXERCISE TESTING DISJUNCTIVE AND DILEMMATIC ARGUMENTS.
(1) If the arithmetic contains useful facts, it will help to good citizenship; and if it trains the powers of reason, it will help to good citizenship,
But the arithmetic either contains useful facts or trains the powers of reason,
Hence it will help to good citizenship.
This is a simple constructive dilemma in which the minor premise affirms the antecedents. The argument is, therefore, valid since it conforms to the rules of the hypothetical syllogism. The fact that the minor premise may not be a perfect disjunctive does not invalidate the conclusion, inasmuch as it is perfectly obvious that if the arithmetic fulfilled both the requirements of the antecedents, the conclusion would still obtain. It may, therefore, be inferred that if the dilemma conforms to the rules of the hypothetical argument, it is valid, though the disjunctive proposition which it contains may not be strictly logical.
(2) A man is either temperate or intemperate; and, as I have seen you drunk several times, I conclude that you are intemperate.
Arranged logically.
A man is either temperate or intemperate,
You are not temperate,
∴ You are intemperate.
It would seem that the major premise is a logical disjunctive, since temperate and intemperate indicate that the alternatives are mutually exclusive and the enumeration complete. And since the minor premise denies one alternative while the conclusion affirms the other, we may infer that the argument is valid.
(3) If a man is honest, he will either pay his debts or explain; but this fellow paid no heed to the repeated notifications.
Arranged logically.
If a man is honest, he will pay his debts; and if he is honest, he will explain in case he cannot pay,
This man neither paid his debt, nor explained,
∴ This man is not honest.
This is a simple destructive dilemma, and since the minor premise denies the consequents it is valid.
(4) A voter must either favor protection or free trade; and since you do not favor protection, you must be a free trader. The disjunctive is not logical as one might believe in universal reciprocity. The argument is, therefore, invalid. Why?
(5) If a man were loyal, he would not be unduly critical; and if he were wise, he would not be too loquacious; but I find this clerk has been both unduly critical and too loquacious; hence I consider that he has been not only unwise but strikingly disloyal.
This complex dilemma is valid since the minor premise denies the two consequents.